Why Does tan x Have This Domain?

[shihab-kol]

I found in a book that the domain of tan x was {(2n+1)π/2 , n∈I}
The graph however shows that for every value of x , the function takes on a value .So, why is the domain like this?

 

[fresh_42]

I found in a book that the domain of tan x was {(2n+1)π/2 , n∈I}
The graph however shows that for every value of x , the function takes on a value .So, why is the domain like this?

$\tan(x) = \frac{\sin(x)}{\cos(x)}$ so whenever $\cos(x) =0$ then $\tan(x)$ isn't defined.

 

[jbriggs444]

I found in a book that the domain of tan x was {(2n+1)π/2 , n∈I}

That set is the complement of the domain of the tan function -- the set of x values where tan x is undefined.

 

[shihab-kol]

So that set does not reflect the defined values of the function,just the undefined ones. Right?
Correct me if I am wrong.

 

[Mark44]

So that set does not reflect the defined values of the function,just the undefined ones. Right?
Correct me if I am wrong.

The set you wrote in post #1 is not the defined values of the function. The range of the tangent function (set of all output values) is all real numbers. That set in post #1 lists (by a formula) all of the numbers that are not in the domain of tan(x).